Digitization of signals is a problem in information systems where the noise level may vary across the dynamic range of the information signal. For example, in X-ray imaging devices there is an inherent noise associated with the statistical uncertainty of the X-ray photon emissions and absorption which increases with increasing number of photons finally detected. Typically, after passing through a body to be imaged the X-rays are detected by an image intensifier, which converts the X-ray pattern into a visible image that is scanned by a video camera whose output is used for further processing of the image information. This video camera introduces into the system additional electronic noise which is approximately constant over the range of the image signal. The combined noise, the photon noise and the electronic noise, is therefore variable over the operating range of the system and can be considered as the inherent noise associated with the analog signal to be digitized. The various noise factors are typically expressed in terms of the standard deviation.
The digitization process intrinsically adds an error, the RMS value of which is proportional to the width of the digitization (quantization) interval. This error can be dealt with as a digitization noise, which furtherly combines with the inherent noise of the analog signal. To preserve the information content of the signal throughout its full dynamic range, the overall noise of the digitized signal should not exceed the inherent analog signal noise by more than a few percent. In other terms, because of the variable nature of the noise, the digitization interval must be related to the noise in that smaller intervals are required with smaller inherent noise signals and larger intervals with larger inherent noise signals. Thus the digitizing interval must be made sufficiently small to properly code the signals with reference to its minimum inherent noise. This results in the over coding of the signal where it carries higher inherent noise whenever no provision is made to adapt the digitization interval. This is inefficient and adds entropy to the digitized data in excess of the information content of the signal. For example, a sufficiently small digitization interval to satisfactorily code an X-ray video signal throughout its full dynamic range may require as much as a twelve bit analog to digital converter. Further, the subsequent processing equipment will require storing of at least twelve bit words. In addition, the additional entropy of the digitized data adversely affects the data compression obtainable.